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Well-posedness and dynamics of stochastic fractional model for nonlinear optical fiber materials. (English) Zbl 1346.37061

Summary: The current paper is devoted to the well-posedness and dynamics of the stochastic coupled fractional Ginzburg-Landau equation, which describes a class of nonlinear optical fiber materials with active and passive coupled cores. By the commutation estimates and Fourier-Galerkin approximation, the global existence of weak solutions and the uniqueness criterion are established. Moreover, the existence of a global attractor is shown. Finally, we consider the long-time behavior of the stochastic coupled fractional Ginzburg-Landau equation (SCFGL) with multiplicative noise, and prove the existence of a random attractor for the random dynamical system generated by the SCFGL equation.

MSC:

37L55 Infinite-dimensional random dynamical systems; stochastic equations
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
35R60 PDEs with randomness, stochastic partial differential equations
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35R11 Fractional partial differential equations
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